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Preserving Symmetries in the Proper Orthogonal Decomposition
SIAM Journal on Scientific Computing, 1993The proper orthogonal decomposition (POD) (also called Karhunen–Loève expansion) has been recently used in turbulence to derive optimally fast converging bases of spatial functions, leading to efficient finite truncations. Whether a finite number of these modes can be used in numerical simulations to derive an “accurate” finite set of ordinary ...
Nadine Aubry +2 more
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The Shifted Proper Orthogonal Decomposition: A Mode Decomposition for Multiple Transport Phenomena [PDF]
SIAM Journal of Scientific Computing, 2018 Transport-dominated phenomena provide a challenge for common mode-based model reduction approaches. We present a model reduction method, which is suited for these kinds of systems. It extends the proper orthogonal decomposition (POD) by introducing time-dependent shifts of the snapshot matrix.
Volker Mehrmann +2 more
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Isogeometric Analysis with Proper Orthogonal Decomposition for Elastodynamics
Communications in Computational Physics, 2021We consider reduced order modelling of elastodynamics with proper orthogonal decomposition and isogeometric analysis, a recent novel and promising discretization method for partial differential equations. The generalized-$α$ method for transient problems is used for additional flexibility in controlling high frequency dissipation.
Richen Li, Qingbiao Wu, Shengfeng Zhu
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On The Hidden Beauty of the Proper Orthogonal Decomposition
Theoretical and Computational Fluid Dynamics, 1991The proper orthogonal decomposition theorem (Loeve (1955)) of probability theory has been proposed and adapted by Lumley (1967) for detecting spatial coherent patterns in turbulent flows. More specifically, the decomposition extracts deterministic functions from second order statistics of a random field and converges optimally fast in the quadratic ...
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Proper Orthogonal Decomposition of Turbulent Channel Flow
2001The technique of the Proper Orthogonal Decomposition (POD) is applied to the case of the turbulent channel flow at Re = 40.000 (based on channel half width). The turbulent flow database is obtained with the use of a finite volume computational code for the numerical integration of the Navier-Stokes equations; for turbulence modeling, the LES approach ...
Alfonsi G. +3 more
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Observations on the Proper Orthogonal Decomposition
1992The Proper Orthogonal Decomposition (P.O.D.), also known as the Karhunen-Loeve expansion, is a procedure for decomposing a stochastic field in an L2 optimal sense. It is used in diverse disciplines from image processing to turbulence. Recently the P.O.D.
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Proper orthogonal decomposition of roof pressure
Journal of Wind Engineering and Industrial Aerodynamics, 1993Abstract This paper illustrates application of the proper orthogonal decomposition in an investigation of the aerodynamic loading on a roof of a low-rise building. Pneumatically averaged pressure in a corner region of the roof, measured for concerning wind, was used in the analysis.
B. Bienkiewicz, H.J. Ham, Y. Sun
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Proper orthogonal decomposition of atomistic flow simulations
Journal of Computational Physics, 2012An adaptive proper orthogonal decomposition based on time windows (WPOD) for analysis of velocity fields from atomistic simulations is presented. The method effectively separates the field into ensemble average and fluctuation components, and can be applied to both stationary and non-stationary flows in simple and complex geometries.
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Spatially compressed spectral proper orthogonal decomposition
Physical Review ERecovering coherent structures from sparse or partially sampled flow field data is inherently challenging, and traditional spectral proper orthogonal decomposition (SPOD) methods are further constrained by high computational cost, memory demands, and limited applicability.
Guanzhong Ma +4 more
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Proper orthogonal decomposition and its applications
Asia-Pacific Journal of Chemical Engineering, 2011AbstractThe proper orthogonal decomposition (POD) has become a very useful tool in the analysis and low‐dimensional modelling of flows. It provides an objective way of identifying the ‘coherent’ structures in a turbulent flow. The application of POD to the case of a thermally driven two‐dimensional flow of air in a horizontal rotating cylinder is ...
Sanjeev Sanghi, Nadeem Hasan
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